An optimized method for rolling the operation curve to reduce the longitudinal impulse of heavy-haul trains

Abstract

The present invention belongs to the technical field of train operation curve optimization, and particularly relates to a rolling optimization method for train operation curves to reduce the longitudinal impulse of heavy-haul trains. The present invention separates the coupler force calculation from the optimization algorithm and designs a double-layer rolling optimization framework. In the top-layer optimization, by establishing a rigid multi-particle model of the train, constructing piecewise constraints on the control variables, and taking train energy conservation, speed tracking performance, and smooth operation as the optimization objectives, the quadratic programming algorithm is selected to solve and obtain the operation curve optimized by multiple objectives. The bottom-layer solution is based on the longitudinal dynamics model of the heavy-haul train, and calculates the coupler force distribution of the train at each position in the optimized operation curve to verify whether the coupler force constraint is satisfied. In the case of non-compliance with the constraint, the traction and electric braking change rates are dynamically adjusted, and the cyclic optimization is carried out again. Finally, the safe, smooth, energy-saving, and on-time operation of the heavy-haul train is realized.

Description

Technical Field

[0001] The invention belongs to the technical field of train operation curve optimization, and particularly relates to a rolling optimization method for an operation curve for reducing the longitudinal impulse of a heavy-haul train. Background Art

[0002] With the rapid development of the economy, the demand for heavy-haul railway freight transportation is increasing day by day. China adopts a development strategy of "simultaneously emphasizing speed, density, and quality"; longer formations and greater traction weights have become one of the development directions of heavy-haul trains; however, improper operation of long-formation heavy-haul trains on complex sections can lead to excessive longitudinal impulses, and even cause accidents such as vehicle coupler breakage and derailment. Secondly, the terrain of heavy-haul lines is complex and the formations of heavy-haul trains are long, which poses strict requirements on drivers' driving. These all greatly affect the safe and efficient operation of trains. Therefore, it is of great significance to study an operation curve optimization method that meets the longitudinal impulse constraints of heavy-haul trains.

[0003] In the current field of heavy-haul train operation curve optimization, most scholars often regard the train as a whole and establish single-particle models, rigid multi-particle models, homogeneous rod models, etc. of the train. These models are simple to construct and easy to solve, but they cannot represent the magnitude of the coupler forces between carriages. In order to measure the safety and smoothness of heavy-haul trains, only the train safety is transformed into speed limit constraints, and the smoothness is transformed into constraints on the change rate of control variables or relative displacements between vehicles. The magnitude and change rate of coupler forces are important indicators for characterizing the safe and smooth operation of trains. Such models cannot directly incorporate the magnitude and change rate of coupler forces as constraints into the optimization process, resulting in some optimized curves still not having good safety and smoothness. Some scholars have established a longitudinal dynamics model of the train based on the characteristics of the coupler buffers of heavy-haul trains, and solved the coupler forces of the train during the optimization calculation process to obtain an optimized curve that meets the longitudinal impulse constraints. However, due to the complex non-linear characteristics of the train longitudinal dynamics model, it greatly increases the solving difficulty of some linear optimization methods; secondly, the longitudinal dynamics model considers the state constraints of all vehicles, resulting in a huge state solution space during the optimization process, making the optimization solving efficiency low. In existing research, many train operation curve optimization methods cannot simultaneously meet the requirements of simple models, solving efficiency, and coupler force calculation. Summary of the Invention

[0004] In order to solve the technical problems existing in the above-mentioned prior art, the invention provides a rolling optimization method for an operation curve for reducing the longitudinal impulse of a heavy-haul train, aiming to solve the technical problem that the prior art fails to effectively limit the magnitude and change rate of the coupler forces of a heavy-haul train, resulting in the inability to effectively guarantee the safety and smoothness of the optimized curve.

[0005] To solve the above technical problems, the technical solution adopted by the invention is as follows:

[0006] An operating curve rolling optimization method for reducing the longitudinal impulse of heavy-haul trains, comprising the following steps:

[0007] S1: Obtain the basic information data of the train, the heavy-haul line data, and the maximum coupler force value of the heavy-haul train;

[0008] S2: Based on the data obtained in S1, establish a rigid multi-particle model of the train and a longitudinal dynamics model of the heavy-haul train;

[0009] S3: Construct piecewise constraints on the change rate of the control quantity and boundary constraints on the state quantity and the control quantity;

[0010] S4: Based on the rigid multi-particle model of the train, piecewise constraints on the control quantity resolution, the state quantity, and the boundary constraints on the control quantity, establish a multi-objective optimization model, and use the quadratic programming algorithm to solve the multi-objective optimization model to obtain the optimized operating curve; and based on the optimized operating curve, obtain the train speed state quantity sequence varying with the discrete position, the train control quantity sequence varying with the discrete position, and the time sequence;

[0011] S5: Based on the train control quantity sequence varying with the discrete position, the time sequence, and the longitudinal dynamics model of the heavy-haul train obtained in S4, calculate the coupler force of the optimized curve, and obtain the coupler force distribution at the front of each vehicle of the train at each discrete moment;

[0012] S6: Based on the coupler force distribution at the front of each vehicle at each discrete moment, obtain the maximum coupler force of the full-section vehicle, and judge whether the maximum coupler force meets the coupler force constraint. If it meets, execute S8; if it does not meet, execute S7;

[0013] S7: Dynamically adjust the change rates of traction and electric braking based on the maximum coupler force. After the adjustment is completed, execute S4;

[0014] S8: Output the optimized operating curve that meets the longitudinal impulse limit, including the train speed state quantity sequence and the train control quantity sequence.

[0015] In the present invention, the coupler force calculation is separated from the optimization algorithm, and a double-layer rolling optimization framework is designed; in the top-level optimization, by establishing a rigid multi-particle model of the train and constructing piecewise constraints on the control quantity, with the energy saving, speed following, and smooth operation of the train as the optimization objectives, the quadratic programming algorithm is selected to solve and obtain the multi-objective optimized operating curve; the bottom-level solution is based on the longitudinal dynamics model of the heavy-haul train, and calculates the coupler force distribution of each position of the train in the optimized operating curve to verify whether it meets the coupler force constraint; in the case of not meeting the constraint, dynamically adjust the change rates of traction and electric braking, and perform cyclic optimization again, finally realizing the safe, smooth, energy-saving, and on-time operation of the heavy-haul train.

[0016] Preferably, the train basic information data includes train traction characteristics, electric braking characteristics, air braking characteristics, basic resistance characteristics, and train formation information;

[0017] The heavy-haul line data includes: gradients, curves, and tunnel lines.

[0018] Preferably, the steps for establishing the rigid multi-particle model of the train are as follows:

[0019] Establish a train kinematic model with the train position as the independent variable:

[0020]

[0021] In the formula: v is the train speed; x is the train position; t is the train running time; F t (v) represents the train traction force; F d (v) represents the electric braking force of the train; F m (v) represents the air braking force of the train; F b (v) represents the basic running resistance of the train; F a (x) represents the additional line resistance of the train; γ is the train gyration coefficient, and M is the total mass of the train;

[0022] The additional line resistance includes gradient, curve, and tunnel additional resistances, and is expressed as:

[0023]

[0024] In the formula: x i is the position of the centroid of the i-th vehicle; w g (x i ) is the unit additional resistance of the gradient at position x i ; w r (x i ) is the unit additional resistance of the curve at position x i ; w s (x i ) is the unit additional resistance of the tunnel at position x i ; M i is the mass of the i-th vehicle; g is the acceleration due to gravity.

[0025] Preferably, the longitudinal dynamics model of the train is as follows:

[0026]

[0027] In the formula: The longitudinal force on the i-th vehicle includes: the front coupler force F ci-1 , the rear coupler force F ci , the basic running resistance F bi , the additional line resistance Fai , Traction force F ti , Electric braking force F di and air braking force F mi ; The first part of the formula represents the longitudinal dynamic model of locomotive vehicles, j1,…,j nl is the sequence of the formation positions where the locomotive is located; The second part of the formula represents the longitudinal dynamic equation of freight vehicles. When i≠j1,…,j nl it means that the vehicle is not a locomotive vehicle but a freight vehicle; Freight vehicles do not have power units, no traction force F ti and electric braking force F di , The drawbar force of the front vehicle of the first vehicle and the drawbar force of the rear vehicle of the last vehicle are 0, that is, F c0 = 0, F cn = 0.

[0028] Preferably, the S3 includes the following steps:

[0029] S3-1: The piecewise constraint of the control quantity change rate includes the change rate constraints of traction and electric braking; The specific construction steps are as follows:

[0030] Divide the train operation interval into N equal-distance steps at equal intervals, N = (X end - X sta ) / Δx, where X sta is the starting position of the train, X end is the ending position of the train operation, and Δx is the distance between two steps; Then the change rate constraints of the traction and electric braking forces at the kth discrete position of the train are:

[0031]

[0032] In the formula: |ΔF t,k | is the traction at the kth discrete point; |ΔF d,k | is the braking change rate at the kth discrete point; F t,k is the traction force at the kth discrete point; F d,k is the braking force at the kth discrete point; δ Ft,k the locomotive traction force at the kth discrete point; δ Fd,k is the change rate constraint of the electric braking force at the kth discrete point;

[0033] S3-2: Construct the boundary constraints of the state and control quantity: Set the constraints of the speed v k , traction force F t,k , braking force F d,kk at the kth discrete point:

[0034]

[0035] In the formula: v k,uThe speed limit for the k-th discrete point, F t,u is the speed v k the traction force of the locomotive below, F d,u is the speed v k the maximum braking force of the locomotive below; and the control quantity satisfies F t,k ·F d,k = 0, that is, the train cannot have traction force and braking force at the same time.

[0036] Preferably, the S4 includes the following steps:

[0037] Establish a multi-objective optimization model:

[0038]

[0039] In the formula: J is the value of the objective function; w e , w v , w s are the weights of energy conservation, speed tracking and smoothness respectively; η t , η d represent the traction motor efficiency and the regenerative braking motor efficiency respectively; F t,k and F d,k represent the traction force and braking force at the k-th discrete point respectively; v k is the speed at the k-th discrete point, v des,k is the target speed at the k-th discrete point;

[0040] Transform the multi-objective optimization model into the form of a standard quadratic programming algorithm for solution, which is expressed as follows:

[0041]

[0042] In the formula: The first part of the quadratic programming algorithm represents the objective function, H is a 3N×3N symmetric matrix, representing the quadratic term coefficient of the above objective function, f is a vector of length 3N, representing the linear term coefficient of the above objective function, x is a vector of length 3N, that is, the state quantity; the second part represents the optimization constraint, Ax = b is the equality constraint, A is an N×3N matrix, b is an N×1 vector; Cx ≤ d is the inequality constraint, C is an N×3N matrix, d is an N×1 vector; l b ≤ x ≤ u b is the state quantity boundary constraint, l b , u b is a 3N×1 vector;

[0043] Based on the standard quadratic programming algorithm, perform optimization to obtain the optimized operation curve, and based on the optimized operation curve, obtain the train speed state quantity sequence V that changes with the discrete position, the train control quantity sequence F that changes with the discrete position, and the time sequence T; where V = {v0, v1,..., vk ,…, v N} , F = {[F t,1 , F d,1 ,…, [F t,k , F d,k ,…, [F t,N , F d,N} , T = {t0, t1, …, t k ,…, t N} .

[0044] Preferably, the S5 includes the following steps:

[0045] S5-1: Obtain a control sequence discrete in time: Discretize the optimized operation curve at equal time intervals into M steps, M = t N / Δt, where t N is the total operation time of the optimized curve, and Δt is the time step; Combine the time series T to map the control sequence F that changes with discrete positions into a control sequence F′ = {[F′ t,1 , F′ d,1 ,…, [F′ t,m , F′ d,m ,…, [F′ t,M , F′ d,M};

[0046] S5-2: Settle the coupler force of the optimized curve: Use the control sequence F′ that changes with discrete time as the input of the longitudinal dynamics model, and based on the train longitudinal dynamics model, use the numerical integration Zhai method to calculate the coupler force of the train:

[0047]

[0048] In the formula: At the m-th discrete time, x m+1 is the displacement at the (m + 1)-th moment; x m is the displacement at the m-th moment; v m+1 is the velocity at the (m + 1)-th moment; v m is the velocity at the m-th moment; A m is the acceleration at the m-th moment; A m-1 is the acceleration at the (m - 1)-th moment; Δt is the time step; ψ and ρ are the control parameters of the Zhai method;

[0049] After calculating the coupler force of the train by the numerical integration Zhai method, obtain the distribution F c of the front coupler forces of each vehicle of the train at each discrete moment, expressed as:

[0050]

[0051] In the formula: F c,mIndicates the distribution of the front coupler forces of each vehicle at the m-th discrete moment, F c,m,i Indicates the magnitude of the front coupler force of the i-th vehicle at the m-th discrete moment.

[0052] Preferably, the S6 includes the following steps:

[0053] According to the distribution of the front coupler forces of each vehicle at each discrete moment of the train, F c , the maximum coupler force of the entire train at the m-th discrete moment is obtained as:

[0054] F cmax,m = max|F c,m |;

[0055] The maximum coupler force F cmax in the optimized operation curve is expressed as:

[0056] F cmax = max{F cmax,1 ,···,F cmax,m ,···,F cmax,M};

[0057] If F cmax ≤ F c,u , then the optimized curve meets the coupler force limit, go to S8, and output the optimized curve;

[0058] If F cmax > F c,u , then the optimized curve does not meet the coupler force limit, go to S7 to dynamically adjust the traction / electric braking force change rate.

[0059] Preferably, the S7 includes the following steps:

[0060] Map the sequence of the maximum coupler forces {F cmax,1 ,…,F cmax,m ,…,F cmax,M} in the optimized operation curve to the sequence of the maximum coupler forces {F cmax,1 ,…,F cmax,k ,…,F cmax,N} at each discrete position; the mapping method is as follows:

[0061] F cmax,k = max{F cmax,m ,···,F cmax,m+b} if x k-1 <x m <···<x m+b ≤ x k (m = 1,2,···,M);

[0062] In the formula: {F cmax,m ,…,Fcmax,m+b} represents the coupler force distribution of the train in the interval from x k-1 to x k . Taking the maximum value represents the maximum coupler force in this interval;

[0063] Search for the sequence of maximum coupler forces {F cmax,1 , …, F cmax,k , …, F cmax,N} at each discrete position in a traversal manner, and adjust the traction and braking force change rate constraints corresponding to the intervals where the coupler force does not meet the coupler force constraint. After the adjustment is completed, execute S4. The adjustment formula is as follows:

[0064]

[0065] In the formula: is the initial traction force constraint value set for the k-th discrete position; is the braking force change rate constraint value set for the k-th discrete position; is the adjusted traction force constraint value at the k-th discrete position; is the adjusted braking force constraint value at the k-th discrete position; κ is a constraint adjustment constant, less than 1; λ represents that in multiple rolling optimization processes, the corresponding interval is determined to not meet the coupler force constraint for the λ-th time.

[0066] The beneficial effects of the present invention include:

[0067] 1. The present invention separates the coupler force calculation from the optimization algorithm and designs a two-layer rolling optimization framework; in the top-level optimization, by establishing a rigid multi-particle model of the train, constructing piecewise constraints on the control variables, with the energy conservation, speed following, and smooth operation of the train as the optimization objectives, selecting the quadratic programming algorithm to solve and obtain the operation curve optimized by multiple objectives; the bottom-level solution is based on the longitudinal dynamics model of the heavy-haul train, and calculates the coupler force distribution of each position in the optimized operation curve through the Zhai method to verify whether it meets the coupler force constraint; in the case of non-compliance, dynamically adjust the traction and electric braking change rates and perform cyclic optimization again, ultimately achieving the safe, smooth, energy-saving, and on-time operation of the heavy-haul train; and compared with the optimization algorithm based on the longitudinal impulse model of the train, the present invention has a faster solution speed.

[0068] 2. The present invention divides the traction and electric braking force change constraints by interval, and precisely reduces the longitudinal impulse force in complex sections by piecewise adjusting the traction and electric braking force change rates.

[0069] 3. The present invention searches for intervals that do not satisfy the coupler force constraint, and uses a method of gradually decreasing to cyclically adjust the traction and electric braking force change rate constraints in the corresponding intervals, so that the finally formed operation curve can meet the coupler force requirement and achieve the optimal train operation curve. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 It is the overall flowchart of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0071] To make the objectives, technical solutions, and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all of the embodiments. Usually, the components of the embodiments of the present application described and illustrated herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the present application claimed, but merely represents selected embodiments of the present application. All other embodiments obtained by those skilled in the art based on the embodiments of the present application without creative efforts fall within the scope of protection of the present application.

[0072] The following combines the attached Figure 1 to further illustrate the embodiments of the present invention:

[0073] Refer to the attached Figure 1 , a rolling optimization method for an operation curve to reduce the longitudinal impulse of a heavy-haul train, including the following steps:

[0074] S1: Obtain the basic train information data, heavy-haul line data, and the maximum coupler force value of the heavy-haul train; the basic train information data includes the train traction characteristics, electric braking characteristics, air braking characteristics, basic resistance characteristics, and train formation information; the heavy-haul line data includes: slopes, curves, and tunnel lines.

[0075] S2: Based on the data obtained in S1, establish a rigid multi-particle model of the train and a longitudinal dynamics model of the heavy-haul train;

[0076] The steps for establishing the rigid multi-particle model of the train are as follows:

[0077] The heavy-haul train is a power-concentrated train, including n l locomotives and n w freight cars, for a total of n = n l + n wA vehicle; the rigid multi - particle model of the train assumes that each vehicle of the train is rigidly connected, with the same speed and unchanged relative position for each vehicle. The additional resistance of the train on the gradient is obtained by summing the additional resistances suffered by each vehicle under different track conditions. A kinematic model of the train with the train position as the independent variable is established:

[0078]

[0079] In the formula: v is the train speed; x is the position of the train; t is the running time of the train; F t (v) represents the tractive force of the train; F d (v) represents the electric braking force of the train; F m (v) represents the air braking force of the train; F b (v) represents the basic running resistance of the train; F a (x) represents the additional track resistance of the train; γ is the train gyration coefficient, and M is the total mass of the train;

[0080] The additional track resistance includes the gradient, curve and tunnel additional resistances, and is expressed as:

[0081]

[0082] In the formula: x i is the position of the centroid of the i - th vehicle; w g (x i ) is the unit additional resistance of the gradient at the position x i ; w r (x i ) is the unit additional resistance of the curve at the position x i ; w s (x i ) is the unit additional resistance of the tunnel at the position x i ; M i is the mass of the i - th vehicle; g is the acceleration due to gravity.

[0083] The longitudinal dynamics model of the train is as follows:

[0084]

[0085] In the formula: the longitudinal dynamics model of the train regards each vehicle as a rigid particle; the longitudinal force suffered by the i - th vehicle includes: the coupler force F ci-1 from the front vehicle, the coupler force F ci from the rear vehicle, the basic running resistance F bi , the additional track resistance F ai , the tractive force F ti , the electric braking force F di and the air braking force F mi; The previous part of the formula represents the longitudinal dynamics model of rolling stock, j1, …, j nl is the sequence of the formation positions where the locomotive is located; the latter part of the formula represents the longitudinal dynamics equation of freight cars. When i ≠ j1, …, j nl it means that the vehicle is not a locomotive vehicle but a freight car; the freight car has no power unit and no traction force F ti and electric braking force F di , the coupler force of the front vehicle of the first vehicle and the coupler force of the rear vehicle of the last vehicle are 0, that is, F c0 = 0, F cn = 0.

[0086] S3: Construct the piecewise constraint of the control variable change rate and the boundary constraints of the state variables and control variables;

[0087] The said S3 includes the following steps:

[0088] S3-1: Construct the piecewise constraint of the control variable change rate: Considering that the train is in special sections such as undulating slopes, small-radius curves, and temporary speed limits, large longitudinal impulses are likely to occur due to frequent switching between traction and braking conditions. By restricting the change rate of the control variable, the longitudinal power of the train can be effectively reduced; however, if the piecewise constraint of the control variable change rate is set to a small constant value, the solution space will be greatly reduced, which has an adverse effect on the solution effect. Therefore, it is set to change with the train position and is dynamically adjusted according to the coupler force distribution of the subsequent train;

[0089] The piecewise constraint of the control variable change rate includes the change rate constraints of traction and electric braking; the specific construction steps are as follows:

[0090] The train operation interval is equally spaced and discretized into N steps, N = (X end - X sta ) / Δx, where X sta is the starting position of the train, X end is the ending position of the train operation, and Δx is the distance between two steps; then the change rate constraints of the traction and electric braking forces at the kth discrete position of the train are:

[0091]

[0092] In the formula: |ΔF t,k | is the traction at the kth discrete point; |ΔF d,k | is the braking change rate at the kth discrete point; F t,k is the traction force at the kth discrete point; F d,k is the braking force at the kth discrete point; δ Ft,k is the locomotive traction force at the kth discrete point; δ Fd,k is the change rate constraint of the electric braking force at the kth discrete point;

[0093] S3-2: Construct the boundary constraints of the state and control variables: Set the speed v of the k-th discrete point k , the tractive force F t,k , the braking force F d,kk constraints:

[0094]

[0095] where: v k,u is the speed limit of the k-th discrete point, F t,u is the tractive force of the locomotive at speed v k , F d,u is the maximum braking force of the locomotive at speed v k ; and the control variable satisfies F t,k ·F d,k = 0, that is, the train cannot have tractive force and braking force at the same time.

[0096] S4: Based on the rigid multi-particle model of the train, the piecewise constraints of the control variable resolution, the state variables, and the boundary constraints of the control variables, establish a multi-objective optimization model, and use the quadratic programming algorithm to solve the multi-objective optimization model to obtain the optimized operation curve; and based on the optimized operation curve, obtain the train speed state variable sequence that changes with the discrete position, the train control variable sequence that changes with the discrete position, and the time sequence;

[0097] The S4 includes the following steps:

[0098] Assume that the train control variable remains unchanged within each discrete interval, and establish a multi-objective optimization model with the weighted sum of the train operation energy consumption, the target speed tracking performance, and the control variable change rate as the objective:

[0099]

[0100] where: J is the objective function value; w e , w v , w s are the weights of energy conservation, speed following performance, and smoothness respectively; η t , η d represent the traction motor efficiency and the regenerative braking motor efficiency respectively; F t,k and F d,k represent the tractive force and the braking force of the k-th discrete point respectively; v k is the speed of the k-th discrete point, v des,k is the target speed of the k-th discrete point;

[0101] Transform the multi-objective optimization model into the form of a standard quadratic programming algorithm for solution, which is expressed as follows:

[0102]

[0103] In the formula: The first part of the quadratic programming algorithm represents the objective function. H is a 3N×3N symmetric matrix, representing the quadratic term coefficient of the above objective function. f is a vector of length 3N, representing the linear term coefficient of the above objective function. x is a vector of length 3N, that is, the state variable. The latter part represents the optimization constraints. Ax = b is the equality constraint, A is an N×3N matrix, and b is an N×1 vector. Cx ≤ d is the inequality constraint, C is an N×3N matrix, and d is an N×1 vector; l b ≤x≤u b is the boundary constraint of the state variable, l b , u b are 3N×1 vectors; The derivation process of the quadratic programming algorithm can be referred to the following literature:

[0104] Bai Baoxue,Xiao Zhuang,Wang Qingyuan,et al.Multi-Objective TrajectoryOptimization for Freight Trains Based on Quadratic Programming[J].Transportation Research Record,2020,2674(11):466-477。

[0105] Based on the standard quadratic programming algorithm for optimization and solution, an optimized operation curve is obtained. Based on the optimized operation curve, a train speed state variable sequence V varying with discrete positions, a train control variable sequence F varying with discrete positions, and a time sequence T are obtained. Among them, V = {v0, v1, …, v k , …, v N}, F = {[F t,1 , F d,1 , …, [F t,k , F d,k , …, [F t,N , F d,N}, T = {t0, t1, …, t k , …, t N}.

[0106] S5: Based on the train control variable sequence, time sequence, and the coupler force of the optimized curve calculated by the longitudinal dynamics model of the heavy-haul train obtained in S4, the coupler force distribution at the front of each vehicle of the train at each discrete moment is obtained;

[0107] The S5 includes the following steps:

[0108] S5-1: Obtain the control sequence discretized with time: The optimized operation curve is discretized into M step lengths at equal time intervals, M = t N / Δt, where t N To optimize the total running time of the curve, Δt is the time step; combined with the time series T, the control sequence F that changes with the discrete position is mapped to the control sequence F' = {[F' t,1 , F' d,1 , …, [F' t,m , F' d,m , …, [F' t,M , F' d,M} that changes with the discrete time. The mapping method is shown as follows:

[0109]

[0110] S5-2: Settlement of the coupler force of the optimized curve: Taking the control sequence F' that changes with the discrete time as the input of the longitudinal dynamics model, based on the train longitudinal dynamics model, the train coupler force is calculated by using the numerical integration Zhai method:

[0111]

[0112] In the formula: at the m-th discrete time, x m+1 is the displacement at the (m + 1)-th moment; x m is the displacement at the m-th moment; v m+1 is the velocity at the (m + 1)-th moment; v m is the velocity at the m-th moment; A m is the acceleration at the m-th moment; A m-1 is the acceleration at the (m - 1)-th moment; Δt is the time step; ψ and ρ are the control parameters of the Zhai method;

[0113] After calculating the train coupler force by using the numerical integration Zhai method, the distribution F c of the front coupler forces of each vehicle of the train at each discrete moment is obtained, which is expressed as:

[0114]

[0115] In the formula: F c,m represents the distribution of the front coupler forces of each vehicle at the m-th discrete moment, and F c,m,i represents the magnitude of the front coupler force of the i-th vehicle at the m-th discrete moment.

[0116] S6: Based on the distribution of the front coupler forces of each vehicle at each discrete moment, the maximum coupler force of the whole section is obtained, and it is judged whether the maximum coupler force meets the coupler force constraint. If it meets, S8 is executed; if not, S7 is executed;

[0117] The said S6 includes the following steps:

[0118] According to the distribution F c, the maximum coupler force of the whole train at the $m$-th discrete moment is obtained as follows:

[0119] $F$ cmax,m $=$ $\max|F$ c,m $|$;

[0120] The maximum coupler force $F$ in the optimized operation curve over the entire interval is expressed as: cmax It is expressed as:

[0121] $F$ cmax $=$ $\max\{F$ cmax,1 , ···, $F$ cmax,m , ···, $F$ cmax,M $\}$;

[0122] During the train operation, the maximum coupler force value of the operation curve over the entire interval should be less than the maximum coupler force limit $F$ c,u , and this limit is affected by the coupler characteristics. Exceeding this value may cause the coupler to break. By verifying whether the coupler force meets the coupler force constraint:

[0123] If $F$ cmax $\leq F$ c,u , then the optimized curve meets the coupler force limit, go to S8, and output the optimized curve;

[0124] If $F$ cmax $> F$ c,u , then the optimized curve does not meet the coupler force limit, go to S7 to dynamically adjust the traction / electric braking force change rate.

[0125] S7: Dynamically adjust the traction and electric braking change rates based on the maximum coupler force. After the adjustment is completed, execute S4;

[0126] The said S7 includes the following steps:

[0127] Map the maximum coupler force sequence $\{F$ cmax,1 , …, $F$ cmax,m , …, $F$ cmax,M $\}$ in the optimized operation curve to the maximum coupler force sequence $\{F$ cmax,1 , …, $F$ cmax,k , …, $F$ cmax,N $\}$ at each discrete position; The mapping method is as follows:

[0128] $F$ cmax,k $=$ $\max\{F$ cmax,m , ···, $F$ cmax,m+b $\}$ if $x$ k-1 $<$ $x$ m $<$ ··· $<$ $x$ m+b $\leq$ $x$ k $(m = 1, 2, ···, M)$;

[0129] In the formula: $\{F$ cmax,m,…,F cmax,m+b} represents the distribution of the coupler forces of the trains within the interval from x k-1 to x k . Taking the maximum value represents the maximum coupler force in this interval;

[0130] Search for the sequence of maximum coupler forces {F cmax,1 ,…,F cmax,k ,…,F cmax,N} at each discrete position in a traversal manner, and adjust the constraint on the rate of change of traction and braking forces corresponding to the interval where the coupler force does not meet the coupler force constraint. After the adjustment is completed, execute S4. The adjustment formula is as follows:

[0131]

[0132] In the formula: is the initial traction force constraint value set for the k-th discrete position; is the constraint value on the rate of change of electric braking force set for the k-th discrete position; is the adjusted traction force constraint value at the k-th discrete position; is the adjusted electric braking force constraint value at the k-th discrete position; κ is a constraint adjustment constant, less than 1; λ represents that in multiple rolling optimization processes, the corresponding interval is determined to not meet the coupler force constraint for the λ-th time.

[0133] S8: Output the optimized operation curve that meets the longitudinal impulse limit, including the sequence of train speed state variables and the sequence of train control variables.

[0134] The present invention separates the coupler force calculation from the optimization algorithm and designs a two-layer rolling optimization framework; in the top-level optimization, by establishing a rigid multi-particle model of the train, constructing piecewise constraints on the control variables, with the energy conservation, speed tracking, and smooth operation of the train as the optimization objectives, select the quadratic programming algorithm to solve and obtain the operation curve optimized for multiple objectives; the bottom-level solution is based on the longitudinal dynamics model of the heavy-haul train, and calculate the distribution of the coupler forces of the train at each position in the optimized operation curve to verify whether the coupler force constraint is met; in the case of non-compliance, dynamically adjust the rates of change of traction and electric braking, and perform cyclic optimization again, ultimately achieving the safe, smooth, energy-saving, and on-time operation of the heavy-haul train.

[0135] The above embodiments only represent the specific implementation manners of the present application. The description is relatively specific and detailed, but it should not be construed as a limitation on the protection scope of the present application. It should be noted that for those of ordinary skill in the art, without departing from the concept of the technical solution of the present application, several deformations and improvements can still be made, and these all belong to the protection scope of the present application.

Claims

1. An operating curve rolling optimization method for reducing the longitudinal impulse of heavy-haul trains, characterized in that, The steps include the following: S1: Obtain the basic train information data, heavy-haul line data, and the maximum coupler force value of the heavy-haul train; S2: Based on the data obtained in S1, establish a rigid multi-particle model of the train and a longitudinal dynamics model of the heavy-haul train; S3: Construct piecewise constraints on the change rate of the control quantity and boundary constraints on the state quantity and the control quantity; S4: Based on the rigid multi-particle model of the train, piecewise constraints on the control quantity resolution, state quantity, and boundary constraints on the control quantity, establish a multi-objective optimization model, and use the quadratic programming algorithm to solve the multi-objective optimization model to obtain the optimized operation curve; and based on the optimized operation curve, obtain the train speed state quantity sequence varying with the discrete position, the train control quantity sequence varying with the discrete position, and the time sequence; S5: Based on the train control quantity sequence varying with the discrete position, the time sequence, and the longitudinal dynamics model of the heavy-haul train obtained in S4, calculate the coupler force of the optimized curve, and obtain the coupler force distribution at the front of each vehicle of the train at each discrete moment; S6: Based on the coupler force distribution at the front of each vehicle at each discrete moment, obtain the maximum coupler force of the full-section train, and judge whether the maximum coupler force meets the coupler force constraint. If it meets, execute S8; if it does not meet, execute S7; S7: Dynamically adjust the change rates of traction and electric braking based on the maximum coupler force. After the adjustment is completed, execute S4; S8: Output the optimized operation curve that meets the longitudinal impulse limit, including the train speed state quantity sequence and the train control quantity sequence.

2. The rolling optimization method for the operation curve to reduce the longitudinal impulse of a heavy-haul train according to claim 1, characterized in that The basic train information data includes the train traction characteristics, electric braking characteristics, air braking characteristics, basic resistance characteristics, and train formation information; The heavy-haul line data includes: slopes, curves, and tunnel lines.

3. The rolling optimization method for the operation curve to reduce the longitudinal impulse of a heavy-haul train according to claim 1, characterized in that, The steps for establishing the rigid multi-particle model of the train are as follows: Establish a train kinematic model with the train position as the independent variable: Where: v is the train speed; x is the position of the train; t is the train operation time; F t (v) represents the tractive force of the train; F d (v) represents the electric braking force of the train; F m (v) represents the air braking force of the train; F b (v) represents the basic running resistance of the train; F a (x) represents the additional line resistance of the train; γ is the train gyration coefficient, and M is the total mass of the train; The additional line resistance includes slope, curve, and tunnel additional resistances, which is expressed as: where: x i is the position of the centroid of the i-th vehicle; w g (x i ) is the unit additional resistance of the ramp at position x i ; w r (x i ) is the unit additional resistance of the curve at position x i ; w s (x i ) is the unit additional resistance of the tunnel at position x i ; M i is the mass of the i-th vehicle; g is the acceleration due to gravity.

4. A rolling optimization method for the operation curve to reduce the longitudinal impulse of a heavy-haul train according to claim 1, characterized in that, The longitudinal dynamics model of the train is as follows: In the formula: the longitudinal force on the i-th vehicle includes: the front coupler force F ci-1 , the rear coupler force F ci , the basic running resistance F bi , the additional line resistance F ai , the tractive force F ti , the electric braking force F di and the air braking force F mi ; the first part of the formula represents the longitudinal dynamics model of locomotives and rolling stock, j1,…,j nl is the sequence of the formation positions where the locomotive is located; the second part of the formula represents the longitudinal dynamics equation of freight cars. When i≠j1,…,j nl it means that the vehicle is not a locomotive or rolling stock but a freight car; a freight car has no power unit, no tractive force F ti and no electric braking force F di . The front coupler force of the first vehicle and the rear coupler force of the last vehicle are 0, that is, F c0 = 0, F cn = 0.

5. A rolling optimization method for the operation curve to reduce the longitudinal impulse of a heavy-haul train according to claim 1, characterized in that, S3 includes the following steps: S3-1: The piecewise constraints on the change rate of the control quantity include the change rate constraints of traction and electric braking; the specific construction steps are as follows: The train operation interval is equally spaced and discretized into N steps, where N = (X end - X sta ) / Δx, where X sta is the starting position of the train, X end is the ending position of the train operation, and Δx is the distance between two steps; then the rate of change constraints of the traction and electric braking forces of the train at k discrete positions are: where: |ΔF t,k | is the traction at the k-th discrete point; |ΔF d,k | is the braking change rate at the k-th discrete point; F t,k is the traction force at the k-th discrete point; F d,k is the braking force at the k-th discrete point; δ Ft,k the locomotive traction force at the k-th discrete point; δ Fd,k is the constraint of the electric braking force change rate at the k-th discrete point; S3-2: Construct boundary constraints for the state and control quantity: Set the velocity v of the k-th discrete point k , the traction force F t,k , the braking force F d,kk constraints: where: v k,u is the speed limit of the k-th discrete point, F t,u is the locomotive traction force at speed v k and F d,u is the maximum braking force of the locomotive at speed v k and the control quantity satisfies F t,k ·F d,k = 0, that is, the train cannot have traction force and braking force at the same time.

6. A rolling optimization method for an operating curve to reduce the longitudinal impulse of a heavy-haul train according to claim 1, characterized in that S4 includes the following steps: Establish a multi-objective optimization model: where: J is the objective function value; w e and w v and w s are the weights of energy conservation, speed tracking performance, and smoothness, respectively; η t and η d represent the electromechanical efficiency of the traction motor and the electromechanical efficiency of the regenerative brake, respectively; F t,k and F d,k represent the traction force and braking force at the k-th discrete point, respectively; v k is the speed at the k-th discrete point, and v des,k is the target speed at the k-th discrete point. Convert the multi-objective optimization model into the form of a standard quadratic programming algorithm for solution, which is expressed as follows: In the formula: The first part of the quadratic programming algorithm represents the objective function. H is a 3N×3N symmetric matrix, representing the quadratic term coefficient of the above objective function. f is a vector of length 3N, representing the linear term coefficient of the above objective function. x is a vector of length 3N, that is, the state variable. The second part represents the optimization constraints. Ax = b is the equality constraint, A is an N×3N matrix, and b is an N×1 vector. Cx ≤ d is the inequality constraint, C is an N×3N matrix, and d is an N×1 vector; b l ≤ x ≤ u b is the boundary constraint of the state variable, l b , u b is a 3N×1 vector; Optimize and solve based on the standard quadratic programming algorithm to obtain the optimized operation curve. Based on the optimized operation curve, obtain the train speed state quantity sequence V that varies with the discrete position, the train control quantity sequence F that varies with the discrete position, and the time sequence T. Among them, V = {v0, v1, …, v k , …, v N}, F = {[F t,1 , F d,1 , …, [F t,k , F d,k , …, [F t,N , F d,N}, T = {t0, t1, …, t k , …, t N}.

7. A rolling optimization method for the operation curve to reduce the longitudinal impulse of a heavy-haul train according to claim 1, characterized in that S5 includes the following steps: S5-1: Obtain a discrete control sequence over time: Discretize the optimized operation curve at equal time intervals into M steps, where M = t N / Δt, where t N is the total running time of the optimized curve and Δt is the time step; Map the control sequence F that varies with the discrete position to a control sequence F′ that varies with the discrete time in combination with the time series T, F′ = {[F′ t,1 , F′ d,1 , …, [F′ t,m , F′ d,m , …, [F′ t,M , F′ d,M}; S5-2: Calculate the coupler force of the optimized curve: Take the control sequence F′ varying with the discrete time as the input of the longitudinal dynamics model, and based on the longitudinal dynamics model of the train, use the numerical integration method to calculate the coupler force of the train; where: at the m-th discrete time, x m+1 is the displacement at the (m + 1)-th moment; x m is the displacement at the m-th moment; v m+1 is the velocity at the (m + 1)-th moment; v m is the velocity at the m-th moment; A m is the acceleration at the m-th moment; A m-1 is the acceleration at the (m - 1)-th moment; Δt is the time step; ψ and ρ are the control parameters of the Zhai method; After calculating the coupler forces of the train by means of numerical integration, the distribution of the front coupler forces of each vehicle at each discrete moment of the train, denoted as F, is obtained. c , is expressed as: where: F c,m represents the distribution of the front coupler forces of each vehicle at the m-th discrete moment, F c,m,i represents the magnitude of the front coupler force of the i-th vehicle at the m-th discrete moment.

8. A rolling optimization method for the operation curve to reduce the longitudinal impulse of a heavy-haul train according to claim 1, characterized in that S6 includes the following steps: According to the distribution of the front coupler forces F of each vehicle at each discrete moment of the train c , the maximum coupler force of the entire train at the m-th discrete moment of the train is obtained as follows: F cmax,m = max|F c,m |; The maximum coupler force F in the entire range in the optimized operation curve cmax is expressed as: F cmax = max{F cmax,1 , ···, F cmax,m , ···, F cmax,M}; If F cmax ≤ F c,u , then the optimized curve meets the coupler force limit, go to S8 and output the optimized curve; If F cmax > F c,u , then the optimized curve does not meet the coupler force limit, and it transfers to S7 to dynamically adjust the traction / electric braking force change rate.

9. A rolling optimization method for the operation curve to reduce the longitudinal impulse of a heavy-haul train according to claim 1, characterized in that S7 includes the following steps: Map the sequence of the maximum coupler forces {F cmax,1 , …, F cmax,m , …, F cmax,M} in the optimized operation curve to the sequence of the maximum coupler forces {F cmax,1 , …, F cmax,k , …, F cmax,N} at each discrete position; the mapping method is as follows: F cmax,k = max{F cmax,m , ···, F cmax,m+b} if x k-1 <x m <···<x m+b ≤x k (m = 1, 2, ···, M); Where: {F cmax,m , …, F cmax,m+b} represents the distribution of the coupler forces of the trains in the interval from x k-1 to x k . Taking the maximum value represents the maximum coupler force in this interval; Search for the intervals where the coupler forces in the maximum coupler force sequences {F cmax,1 , …, F cmax,k , …, F cmax,N} at each discrete position do not satisfy the coupler force constraint, adjust the traction and braking force change rate constraints corresponding to the intervals where the coupler force constraint is not satisfied, and execute S4 after the adjustment. The adjustment formula is as follows: Wherein: The initial traction force constraint value set for the k-th discrete position; The electric braking force change rate constraint value set for the k-th discrete position; The traction force constraint value of the adjusted k-th discrete position; The electric braking force constraint value of the adjusted k-th discrete position; κ is a constraint adjustment constant, less than 1; λ represents that in multiple rolling optimization processes, the corresponding interval is determined to not satisfy the coupler force constraint for the λ-th time.

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